Trump and May held a joint press conference after meeting at the prime minister's country home in Chequers on Friday.
As the interview began to make waves, Trade Secretary Liam Fox tweeted from the Blenheim Palace event about how Trump had talked "so positively about United Kingdom and USA trade".
In an antagonistic interview with The Sun, the U.S. president lashed out at Sadiq Khan, accusing him of doing a "terrible" job, claimed Boris Johnson would make a great Prime Minister and made it clear he was very aware of the giant inflatable Trump baby due to fly above Parliament today - and would be avoiding London.
On Thursday evening, Donald and Melania Trump joined May and her husband, Philip May, for a black-tie dinner at Blenheim Palace, the family home of Sir Winston Churchill, the Independent reported.
Among other issues discussed were Trump's relationship with Russian President Vladimir Putin (with whom Trump will meet at a summit next week), immigration, North Atlantic Treaty Organisation and Brexit.
Trump, as he has before, criticized London's mayor, Sadiq Khan, as having "done a very bad job on terrorism".
Duchess of Cambridge beams in white at Prince Louis' christening
The Duke and Duchess of Sussex - otherwise known as Prince Harry and the former Meghan Markle - were also present at the ceremony. The young royal will wear a handmade replica of the royal christening robe, made by Angela Kelly , the dressmaker to the queen .
Trump also told The Sun that May had ignored his advice on Brexit, telling the paper that "I would have done it much differently".
It seems likely that Trump's complaint will focus on two words that appear inside quotation marks in the tabloid's headline - the idea that May "wrecked it", referring to Brexit.
LONDON ― An enormous blimp depicting President Donald Trump as a baby throwing a temper tantrum set sail over the city Friday morning. "He obviously likes me and says very good things about me", he added.
"She's a total professional", Trump said.
Trump also lashed out at U.S. broadcasters CNN and refused to take a question from them. "And unfortunately there was a story that was done, which was generally fine, but it didn't put in what I said about the prime minister, and I said tremendous things".
Trump claimed that he didn't criticize May in his interview with The Sun, and he even called the report "fake news".
North Atlantic Treaty Organisation insists it's united at end of raucous, divisive summit
Lithuanian President Dalia Grybauskaite told reporters she's comfortable with the Trump-Putin summit, but it "depends very much on outcomes".
Trump has always been a supporter of Brexit and has expressed enthusiasm for a wide-ranging trade deal with Britain after it leaves the European Union, something heralded by Brexit supporters as being one of the great benefits of exiting the bloc. "I think they agree with me on immigration", he told reporters in Brussels.
"There is no stronger alliance than that of our special relationship with the US and there will be no alliance more important in the years ahead", May said in a statement.
As the Trumps dined with the Mays, protests in the British capital took place outside Winfield House, the residence of US Ambassador Woody Johnson.
"I told her how to do it".
Trump also said that he was "very saddened" to see Johnson was leaving government and said he hoped "he goes back in at some point. I think he has done a very bad job on terrorism". "Now he might not like the current president, but I represent the United States", Trump said.
Thai cave mission successfully rescues soccer team and their coach
Some divers rescuing the boys trapped in a cave in northern Thailand have traversed about 10 miles over the past two days. Authorities have said the mission could take up to four days to complete and heavy rain is forecast in the coming days.